where \(\phi \)  encodes a `phasonic' continuous shift of the potential, and \(\beta \)  interpolates between two known limiting cases, namely, for \(\beta \rightarrow 0\) , we obtain the Harper-Aubry-André cosine modulation [1]}, [2]}, up to a constant shift \(\left[\cos {(2\pi x/\tau + \phi )} -\cos {(\pi /\tau )}\right]\) , and for \(\beta \rightarrow \infty \)  the Fibonacci sequence is reached with alternating values of \(\pm 1\)  [3]}, [4]}, [5]}. Note that in dimensions \(D>1\)  the quasiperiodic potential functions become more complex and include also rotational symmetries that are forbidden for periodic crystals [6]}, see Fig. REF (a).
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